Geodesic
Polynomial deformations of the Lie algebras $sl(2)$ in problems of quantum optics
Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 1, pp. 3-19

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It is shown that specific (polynomial) deformations of Lie algebras arise naturally as dynamical symmetry algebras $g^{ds}$ of second-quantized models with nonquadratic Hamiltonians $H$ invariant with respect to certain groups $G^{\text {inv}}(H)$. Such deformations $sl_ d(2)$ of the Lie algebras $sl(2)$ are found in a number of models of quantum optics (multiphoton processes, generalized Dicke model, and frequency conversion), and ways to apply thes $sl(2)$ formalism to the solution of physics problems are indicated. 
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     author = {V. P. Karassiov},
     title = {Polynomial deformations of the {Lie} algebras $sl(2)$ in problems of quantum optics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     number = {1},
     year = {1993},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1993_95_1_a0/}
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V. P. Karassiov. Polynomial deformations of the Lie algebras $sl(2)$ in problems of quantum optics. Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 1, pp. 3-19. http://geodesic.mathdoc.fr/item/TMF_1993_95_1_a0/